D02UAF obtains the Chebyshev coefficients of a function discretized on Chebyshev Gauss–Lobatto points. The set of discretization points on which the function is evaluated is usually obtained by a previous call to
D02UCF.
D02UAF computes the coefficients
${c}_{\mathit{j}}$, for
$\mathit{j}=1,2,\dots ,n+1$, of the interpolating Chebyshev series
which interpolates the function
$f\left(x\right)$ evaluated at the Chebyshev Gauss–Lobatto points
Here
${T}_{j}\left(\stackrel{-}{x}\right)$ denotes the Chebyshev polynomial of the first kind of degree
$j$ with argument
$\stackrel{-}{x}$ defined on
$\left[-1,1\right]$. In terms of your original variable,
$x$ say, the input values at which the function values are to be provided are
where
$b$ and
$a$ are respectively the upper and lower ends of the range of
$x$ over which the function is required.
If on entry
${\mathbf{IFAIL}}=0$ or
$-1$, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The Chebyshev coefficients computed should be accurate to within a small multiple of machine precision.
D02UAF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
D02UAF makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.